It sounds as if you are talking about your grandparents.

Do you have your father's birth certificate - this will give you the full names of his parents including the maiden name of your grandmother.

Next get your granparents marriage certificate. This will give you the date of the marriage plus, with a bit of luck, their age at marriage.

Next get your grandparents birth certificates.
By now you are probably into the period covered by the publicaly available census records.